Note
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KL-SVD on Burgers equation¶
Example using KL-SVD on solutions of the Burgers equation.
from __future__ import annotations
import matplotlib.pyplot as plt
from gemseo import configure_logger
from gemseo.mlearning.transformers.dimension_reduction.klsvd import KLSVD
from gemseo.problems.dataset.burgers import create_burgers_dataset
configure_logger()
<RootLogger root (INFO)>
Load dataset¶
dataset = create_burgers_dataset(n_samples=20)
dataset
| GROUP | inputs | outputs | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| VARIABLE | t | u_t | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| COMPONENT | 0 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 | 31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 | ... | 461 | 462 | 463 | 464 | 465 | 466 | 467 | 468 | 469 | 470 | 471 | 472 | 473 | 474 | 475 | 476 | 477 | 478 | 479 | 480 | 481 | 482 | 483 | 484 | 485 | 486 | 487 | 488 | 489 | 490 | 491 | 492 | 493 | 494 | 495 | 496 | 497 | 498 | 499 | 500 |
| 0 | 0.000000 | -8.610583e-43 | 0.012566 | 0.025133 | 0.037699 | 0.050265 | 0.062832 | 0.075398 | 0.087965 | 0.100531 | 0.113097 | 0.125664 | 0.138230 | 0.150796 | 0.163363 | 0.175929 | 0.188496 | 0.201062 | 0.213628 | 0.226195 | 0.238761 | 0.251327 | 0.263894 | 0.276460 | 0.289027 | 0.301593 | 0.314159 | 0.326726 | 0.339292 | 0.351858 | 0.364425 | 0.376991 | 0.389557 | 0.402124 | 0.414690 | 0.427257 | 0.439823 | 0.452389 | 0.464956 | 0.477522 | ... | -0.490088 | -0.477522 | -0.464956 | -0.452389 | -0.439823 | -0.427257 | -0.414690 | -0.402124 | -0.389557 | -0.376991 | -0.364425 | -0.351858 | -0.339292 | -0.326726 | -0.314159 | -0.301593 | -0.289027 | -0.276460 | -0.263894 | -0.251327 | -0.238761 | -0.226195 | -0.213628 | -0.201062 | -0.188496 | -0.175929 | -0.163363 | -0.150796 | -0.138230 | -0.125664 | -0.113097 | -0.100531 | -0.087965 | -0.075398 | -0.062832 | -0.050265 | -0.037699 | -0.025133 | -0.012566 | 8.610583e-43 |
| 1 | 0.105263 | -3.809524e-01 | -0.369583 | -0.358213 | -0.346844 | -0.335474 | -0.324105 | -0.312735 | -0.301365 | -0.289996 | -0.278626 | -0.267257 | -0.255887 | -0.244517 | -0.233148 | -0.221778 | -0.210409 | -0.199039 | -0.187670 | -0.176300 | -0.164930 | -0.153561 | -0.142191 | -0.130822 | -0.119452 | -0.108083 | -0.096713 | -0.085343 | -0.073974 | -0.062604 | -0.051235 | -0.039865 | -0.028496 | -0.017126 | -0.005756 | 0.005613 | 0.016983 | 0.028352 | 0.039722 | 0.051091 | ... | -0.824366 | -0.812996 | -0.801627 | -0.790257 | -0.778887 | -0.767518 | -0.756148 | -0.744779 | -0.733409 | -0.722040 | -0.710670 | -0.699300 | -0.687931 | -0.676561 | -0.665192 | -0.653822 | -0.642453 | -0.631083 | -0.619713 | -0.608344 | -0.596974 | -0.585605 | -0.574235 | -0.562866 | -0.551496 | -0.540126 | -0.528757 | -0.517387 | -0.506018 | -0.494648 | -0.483279 | -0.471909 | -0.460539 | -0.449170 | -0.437800 | -0.426431 | -0.415061 | -0.403692 | -0.392322 | -3.809524e-01 |
| 2 | 0.210526 | -6.956522e-01 | -0.685271 | -0.674890 | -0.664509 | -0.654129 | -0.643748 | -0.633367 | -0.622986 | -0.612605 | -0.602224 | -0.591843 | -0.581462 | -0.571081 | -0.560700 | -0.550319 | -0.539938 | -0.529558 | -0.519177 | -0.508796 | -0.498415 | -0.488034 | -0.477653 | -0.467272 | -0.456891 | -0.446510 | -0.436129 | -0.425748 | -0.415367 | -0.404987 | -0.394606 | -0.384225 | -0.373844 | -0.363463 | -0.353082 | -0.342701 | -0.332320 | -0.321939 | -0.311558 | -0.301177 | ... | -1.100508 | -1.090127 | -1.079746 | -1.069365 | -1.058984 | -1.048603 | -1.038222 | -1.027841 | -1.017461 | -1.007080 | -0.996699 | -0.986318 | -0.975937 | -0.965556 | -0.955175 | -0.944794 | -0.934413 | -0.924032 | -0.913651 | -0.903270 | -0.892890 | -0.882509 | -0.872128 | -0.861747 | -0.851366 | -0.840985 | -0.830604 | -0.820223 | -0.809842 | -0.799461 | -0.789080 | -0.778699 | -0.768319 | -0.757938 | -0.747557 | -0.737176 | -0.726795 | -0.716414 | -0.706033 | -6.956522e-01 |
| 3 | 0.315789 | -9.600000e-01 | -0.950450 | -0.940899 | -0.931349 | -0.921798 | -0.912248 | -0.902697 | -0.893147 | -0.883596 | -0.874046 | -0.864496 | -0.854945 | -0.845395 | -0.835844 | -0.826294 | -0.816743 | -0.807193 | -0.797642 | -0.788092 | -0.778542 | -0.768991 | -0.759441 | -0.749890 | -0.740340 | -0.730789 | -0.721239 | -0.711689 | -0.702138 | -0.692588 | -0.683037 | -0.673487 | -0.663936 | -0.654386 | -0.644835 | -0.635285 | -0.625735 | -0.616184 | -0.606634 | -0.597083 | ... | -1.332467 | -1.322917 | -1.313366 | -1.303816 | -1.294265 | -1.284715 | -1.275165 | -1.265614 | -1.256064 | -1.246513 | -1.236963 | -1.227412 | -1.217862 | -1.208311 | -1.198761 | -1.189211 | -1.179660 | -1.170110 | -1.160559 | -1.151009 | -1.141458 | -1.131908 | -1.122358 | -1.112807 | -1.103257 | -1.093706 | -1.084156 | -1.074605 | -1.065055 | -1.055504 | -1.045954 | -1.036404 | -1.026853 | -1.017303 | -1.007752 | -0.998202 | -0.988651 | -0.979101 | -0.969550 | -9.600000e-01 |
| 4 | 0.421053 | -1.185185e+00 | -1.176342 | -1.167499 | -1.158656 | -1.149813 | -1.140970 | -1.132127 | -1.123284 | -1.114441 | -1.105598 | -1.096755 | -1.087912 | -1.079069 | -1.070226 | -1.061383 | -1.052540 | -1.043697 | -1.034854 | -1.026011 | -1.017168 | -1.008325 | -0.999482 | -0.990639 | -0.981796 | -0.972953 | -0.964110 | -0.955267 | -0.946424 | -0.937581 | -0.928738 | -0.919895 | -0.911052 | -0.902209 | -0.893366 | -0.884523 | -0.875680 | -0.866837 | -0.857994 | -0.849151 | ... | -1.530062 | -1.521219 | -1.512376 | -1.503533 | -1.494690 | -1.485847 | -1.477004 | -1.468161 | -1.459318 | -1.450475 | -1.441632 | -1.432789 | -1.423946 | -1.415103 | -1.406260 | -1.397417 | -1.388574 | -1.379731 | -1.370888 | -1.362045 | -1.353202 | -1.344359 | -1.335516 | -1.326673 | -1.317830 | -1.308987 | -1.300144 | -1.291301 | -1.282458 | -1.273615 | -1.264772 | -1.255929 | -1.247086 | -1.238243 | -1.229400 | -1.220557 | -1.211714 | -1.202871 | -1.194028 | -1.185185e+00 |
| 5 | 0.526316 | -1.379310e+00 | -1.371077 | -1.362844 | -1.354611 | -1.346378 | -1.338145 | -1.329912 | -1.321678 | -1.313445 | -1.305212 | -1.296979 | -1.288746 | -1.280513 | -1.272280 | -1.264046 | -1.255813 | -1.247580 | -1.239347 | -1.231114 | -1.222881 | -1.214648 | -1.206414 | -1.198181 | -1.189948 | -1.181715 | -1.173482 | -1.165249 | -1.157016 | -1.148782 | -1.140549 | -1.132316 | -1.124083 | -1.115850 | -1.107617 | -1.099384 | -1.091150 | -1.082917 | -1.074684 | -1.066451 | ... | -1.700349 | -1.692128 | -1.683904 | -1.675679 | -1.667451 | -1.659222 | -1.650993 | -1.642762 | -1.634531 | -1.626299 | -1.618067 | -1.609835 | -1.601603 | -1.593370 | -1.585137 | -1.576905 | -1.568672 | -1.560439 | -1.552206 | -1.543973 | -1.535740 | -1.527507 | -1.519274 | -1.511040 | -1.502807 | -1.494574 | -1.486341 | -1.478108 | -1.469875 | -1.461642 | -1.453409 | -1.445175 | -1.436942 | -1.428709 | -1.420476 | -1.412243 | -1.404010 | -1.395777 | -1.387543 | -1.379310e+00 |
| 6 | 0.631579 | -1.548387e+00 | -1.540685 | -1.532983 | -1.525281 | -1.517579 | -1.509877 | -1.502175 | -1.494473 | -1.486771 | -1.479069 | -1.471367 | -1.463665 | -1.455963 | -1.448261 | -1.440560 | -1.432858 | -1.425156 | -1.417454 | -1.409752 | -1.402050 | -1.394348 | -1.386646 | -1.378944 | -1.371242 | -1.363540 | -1.355838 | -1.348136 | -1.340434 | -1.332732 | -1.325030 | -1.317328 | -1.309626 | -1.301924 | -1.294222 | -1.286520 | -1.278818 | -1.271116 | -1.263414 | -1.255712 | ... | -1.531535 | -1.587522 | -1.631453 | -1.665337 | -1.690955 | -1.709836 | -1.723271 | -1.732331 | -1.737894 | -1.740671 | -1.741236 | -1.740050 | -1.737479 | -1.733815 | -1.729289 | -1.724084 | -1.718345 | -1.712186 | -1.705695 | -1.698945 | -1.691991 | -1.684876 | -1.677635 | -1.670295 | -1.662878 | -1.655399 | -1.647872 | -1.640308 | -1.632714 | -1.625097 | -1.617462 | -1.609812 | -1.602151 | -1.594481 | -1.586805 | -1.579122 | -1.571436 | -1.563746 | -1.556054 | -1.548360e+00 |
| 7 | 0.736842 | -1.696970e+00 | -1.689735 | -1.682499 | -1.675264 | -1.668029 | -1.660794 | -1.653559 | -1.646323 | -1.639088 | -1.631853 | -1.624618 | -1.617383 | -1.610147 | -1.602912 | -1.595677 | -1.588442 | -1.581207 | -1.573972 | -1.566736 | -1.559501 | -1.552266 | -1.545031 | -1.537796 | -1.530560 | -1.523325 | -1.516090 | -1.508855 | -1.501620 | -1.494385 | -1.487149 | -1.479914 | -1.472679 | -1.465444 | -1.458209 | -1.450973 | -1.443738 | -1.436503 | -1.429268 | -1.422033 | ... | 1.621381 | 1.624286 | 1.626100 | 1.626554 | 1.625314 | 1.621967 | 1.616009 | 1.606820 | 1.593654 | 1.575612 | 1.551629 | 1.520461 | 1.480683 | 1.430705 | 1.368816 | 1.293261 | 1.202368 | 1.094725 | 0.969402 | 0.826206 | 0.665921 | 0.490485 | 0.303035 | 0.107777 | -0.090332 | -0.286048 | -0.474371 | -0.651010 | -0.812728 | -0.957479 | -1.084384 | -1.193560 | -1.285879 | -1.362723 | -1.425748 | -1.476707 | -1.517319 | -1.549187 | -1.573751 | -1.592272e+00 |
| 8 | 0.842105 | -1.828571e+00 | -1.821750 | -1.814928 | -1.808106 | -1.801284 | -1.794463 | -1.787641 | -1.780819 | -1.773997 | -1.767176 | -1.760354 | -1.753532 | -1.746710 | -1.739889 | -1.733067 | -1.726245 | -1.719424 | -1.712602 | -1.705780 | -1.698958 | -1.692137 | -1.685315 | -1.678493 | -1.671671 | -1.664850 | -1.658028 | -1.651206 | -1.644384 | -1.637563 | -1.630741 | -1.623919 | -1.617097 | -1.610276 | -1.603454 | -1.596632 | -1.589810 | -1.582989 | -1.576167 | -1.569345 | ... | 1.316236 | 1.323054 | 1.329870 | 1.336686 | 1.343500 | 1.350313 | 1.357123 | 1.363930 | 1.370734 | 1.377533 | 1.384328 | 1.391115 | 1.397895 | 1.404664 | 1.411421 | 1.418163 | 1.424885 | 1.431584 | 1.438253 | 1.444886 | 1.451473 | 1.458005 | 1.464467 | 1.470844 | 1.477114 | 1.483253 | 1.489229 | 1.495004 | 1.500529 | 1.505746 | 1.510581 | 1.514944 | 1.518725 | 1.521787 | 1.523961 | 1.525042 | 1.524779 | 1.522862 | 1.518920 | 1.512501e+00 |
| 9 | 0.947368 | -1.945946e+00 | -1.939493 | -1.933040 | -1.926587 | -1.920134 | -1.913681 | -1.907228 | -1.900775 | -1.894322 | -1.887869 | -1.881416 | -1.874963 | -1.868510 | -1.862057 | -1.855604 | -1.849151 | -1.842698 | -1.836245 | -1.829792 | -1.823339 | -1.816886 | -1.810433 | -1.803980 | -1.797527 | -1.791074 | -1.784621 | -1.778168 | -1.771715 | -1.765262 | -1.758809 | -1.752356 | -1.745903 | -1.739450 | -1.732997 | -1.726544 | -1.720091 | -1.713638 | -1.707185 | -1.700732 | ... | 1.028888 | 1.035341 | 1.041794 | 1.048247 | 1.054700 | 1.061152 | 1.067605 | 1.074058 | 1.080511 | 1.086964 | 1.093417 | 1.099870 | 1.106323 | 1.112776 | 1.119229 | 1.125682 | 1.132135 | 1.138588 | 1.145040 | 1.151493 | 1.157946 | 1.164398 | 1.170851 | 1.177303 | 1.183755 | 1.190207 | 1.196659 | 1.203110 | 1.209562 | 1.216012 | 1.222463 | 1.228912 | 1.235361 | 1.241809 | 1.248256 | 1.254701 | 1.261145 | 1.267586 | 1.274026 | 1.280461e+00 |
| 10 | 1.052632 | -2.051282e+00 | -2.045160 | -2.039038 | -2.032916 | -2.026794 | -2.020672 | -2.014550 | -2.008428 | -2.002305 | -1.996183 | -1.990061 | -1.983939 | -1.977817 | -1.971695 | -1.965573 | -1.959451 | -1.953329 | -1.947207 | -1.941085 | -1.934963 | -1.928840 | -1.922718 | -1.916596 | -1.910474 | -1.904352 | -1.898230 | -1.892108 | -1.885986 | -1.879864 | -1.873742 | -1.867620 | -1.861498 | -1.855376 | -1.849253 | -1.843131 | -1.837009 | -1.830887 | -1.824765 | -1.818643 | ... | 0.770996 | 0.777118 | 0.783240 | 0.789362 | 0.795484 | 0.801606 | 0.807728 | 0.813850 | 0.819973 | 0.826095 | 0.832217 | 0.838339 | 0.844461 | 0.850583 | 0.856705 | 0.862827 | 0.868949 | 0.875071 | 0.881193 | 0.887315 | 0.893437 | 0.899560 | 0.905682 | 0.911804 | 0.917926 | 0.924048 | 0.930170 | 0.936292 | 0.942414 | 0.948536 | 0.954658 | 0.960780 | 0.966902 | 0.973024 | 0.979146 | 0.985269 | 0.991391 | 0.997513 | 1.003635 | 1.009757e+00 |
| 11 | 1.157895 | -2.146341e+00 | -2.140518 | -2.134695 | -2.128871 | -2.123048 | -2.117224 | -2.111401 | -2.105577 | -2.099754 | -2.093931 | -2.088107 | -2.082284 | -2.076460 | -2.070637 | -2.064813 | -2.058990 | -2.053166 | -2.047343 | -2.041520 | -2.035696 | -2.029873 | -2.024049 | -2.018226 | -2.012402 | -2.006579 | -2.000755 | -1.994932 | -1.989109 | -1.983285 | -1.977462 | -1.971638 | -1.965815 | -1.959991 | -1.954168 | -1.948345 | -1.942521 | -1.936698 | -1.930874 | -1.925051 | ... | 0.538264 | 0.544088 | 0.549911 | 0.555735 | 0.561558 | 0.567382 | 0.573205 | 0.579028 | 0.584852 | 0.590675 | 0.596499 | 0.602322 | 0.608146 | 0.613969 | 0.619793 | 0.625616 | 0.631439 | 0.637263 | 0.643086 | 0.648910 | 0.654733 | 0.660557 | 0.666380 | 0.672204 | 0.678027 | 0.683850 | 0.689674 | 0.695497 | 0.701321 | 0.707144 | 0.712968 | 0.718791 | 0.724614 | 0.730438 | 0.736261 | 0.742085 | 0.747908 | 0.753732 | 0.759555 | 7.653786e-01 |
| 12 | 1.263158 | -2.232558e+00 | -2.227006 | -2.221453 | -2.215900 | -2.210348 | -2.204795 | -2.199243 | -2.193690 | -2.188137 | -2.182585 | -2.177032 | -2.171480 | -2.165927 | -2.160375 | -2.154822 | -2.149269 | -2.143717 | -2.138164 | -2.132612 | -2.127059 | -2.121506 | -2.115954 | -2.110401 | -2.104849 | -2.099296 | -2.093744 | -2.088191 | -2.082638 | -2.077086 | -2.071533 | -2.065981 | -2.060428 | -2.054876 | -2.049323 | -2.043770 | -2.038218 | -2.032665 | -2.027113 | -2.021560 | ... | 0.327182 | 0.332735 | 0.338287 | 0.343840 | 0.349393 | 0.354945 | 0.360498 | 0.366050 | 0.371603 | 0.377156 | 0.382708 | 0.388261 | 0.393813 | 0.399366 | 0.404918 | 0.410471 | 0.416024 | 0.421576 | 0.427129 | 0.432681 | 0.438234 | 0.443787 | 0.449339 | 0.454892 | 0.460444 | 0.465997 | 0.471549 | 0.477102 | 0.482655 | 0.488207 | 0.493760 | 0.499312 | 0.504865 | 0.510418 | 0.515970 | 0.521523 | 0.527075 | 0.532628 | 0.538180 | 5.437330e-01 |
| 13 | 1.368421 | -2.311111e+00 | -2.305805 | -2.300500 | -2.295194 | -2.289888 | -2.284582 | -2.279276 | -2.273971 | -2.268665 | -2.263359 | -2.258053 | -2.252747 | -2.247441 | -2.242136 | -2.236830 | -2.231524 | -2.226218 | -2.220912 | -2.215607 | -2.210301 | -2.204995 | -2.199689 | -2.194383 | -2.189078 | -2.183772 | -2.178466 | -2.173160 | -2.167854 | -2.162549 | -2.157243 | -2.151937 | -2.146631 | -2.141325 | -2.136020 | -2.130714 | -2.125408 | -2.120102 | -2.114796 | -2.109491 | ... | 0.134863 | 0.140169 | 0.145475 | 0.150781 | 0.156086 | 0.161392 | 0.166698 | 0.172004 | 0.177310 | 0.182615 | 0.187921 | 0.193227 | 0.198533 | 0.203839 | 0.209144 | 0.214450 | 0.219756 | 0.225062 | 0.230368 | 0.235673 | 0.240979 | 0.246285 | 0.251591 | 0.256897 | 0.262202 | 0.267508 | 0.272814 | 0.278120 | 0.283426 | 0.288731 | 0.294037 | 0.299343 | 0.304649 | 0.309955 | 0.315260 | 0.320566 | 0.325872 | 0.331178 | 0.336484 | 3.417894e-01 |
| 14 | 1.473684 | -2.382979e+00 | -2.377899 | -2.372819 | -2.367739 | -2.362659 | -2.357579 | -2.352499 | -2.347419 | -2.342339 | -2.337259 | -2.332179 | -2.327098 | -2.322018 | -2.316938 | -2.311858 | -2.306778 | -2.301698 | -2.296618 | -2.291538 | -2.286458 | -2.281378 | -2.276298 | -2.271218 | -2.266138 | -2.261058 | -2.255978 | -2.250898 | -2.245818 | -2.240738 | -2.235658 | -2.230578 | -2.225498 | -2.220418 | -2.215338 | -2.210258 | -2.205178 | -2.200098 | -2.195018 | -2.189938 | ... | -0.041089 | -0.036008 | -0.030928 | -0.025848 | -0.020768 | -0.015688 | -0.010608 | -0.005528 | -0.000448 | 0.004632 | 0.009712 | 0.014792 | 0.019872 | 0.024952 | 0.030032 | 0.035112 | 0.040192 | 0.045272 | 0.050352 | 0.055432 | 0.060512 | 0.065592 | 0.070672 | 0.075752 | 0.080832 | 0.085912 | 0.090992 | 0.096072 | 0.101152 | 0.106232 | 0.111312 | 0.116392 | 0.121472 | 0.126552 | 0.131632 | 0.136712 | 0.141792 | 0.146872 | 0.151952 | 1.570324e-01 |
| 15 | 1.578947 | -2.448980e+00 | -2.444107 | -2.439234 | -2.434362 | -2.429489 | -2.424616 | -2.419744 | -2.414871 | -2.409998 | -2.405126 | -2.400253 | -2.395380 | -2.390507 | -2.385635 | -2.380762 | -2.375889 | -2.371017 | -2.366144 | -2.361271 | -2.356399 | -2.351526 | -2.346653 | -2.341781 | -2.336908 | -2.332035 | -2.327163 | -2.322290 | -2.317417 | -2.312545 | -2.307672 | -2.302799 | -2.297927 | -2.293054 | -2.288181 | -2.283309 | -2.278436 | -2.273563 | -2.268691 | -2.263818 | ... | -0.202677 | -0.197804 | -0.192931 | -0.188059 | -0.183186 | -0.178313 | -0.173441 | -0.168568 | -0.163695 | -0.158823 | -0.153950 | -0.149077 | -0.144205 | -0.139332 | -0.134459 | -0.129587 | -0.124714 | -0.119841 | -0.114969 | -0.110096 | -0.105223 | -0.100351 | -0.095478 | -0.090605 | -0.085733 | -0.080860 | -0.075987 | -0.071115 | -0.066242 | -0.061369 | -0.056497 | -0.051624 | -0.046751 | -0.041878 | -0.037006 | -0.032133 | -0.027260 | -0.022388 | -0.017515 | -1.264243e-02 |
| 16 | 1.684211 | -2.509804e+00 | -2.505122 | -2.500441 | -2.495759 | -2.491078 | -2.486396 | -2.481714 | -2.477033 | -2.472351 | -2.467670 | -2.462988 | -2.458306 | -2.453625 | -2.448943 | -2.444262 | -2.439580 | -2.434898 | -2.430217 | -2.425535 | -2.420854 | -2.416172 | -2.411491 | -2.406809 | -2.402127 | -2.397446 | -2.392764 | -2.388083 | -2.383401 | -2.378719 | -2.374038 | -2.369356 | -2.364675 | -2.359993 | -2.355311 | -2.350630 | -2.345948 | -2.341267 | -2.336585 | -2.331904 | ... | -0.351591 | -0.346910 | -0.342228 | -0.337547 | -0.332865 | -0.328183 | -0.323502 | -0.318820 | -0.314139 | -0.309457 | -0.304775 | -0.300094 | -0.295412 | -0.290731 | -0.286049 | -0.281368 | -0.276686 | -0.272004 | -0.267323 | -0.262641 | -0.257960 | -0.253278 | -0.248596 | -0.243915 | -0.239233 | -0.234552 | -0.229870 | -0.225188 | -0.220507 | -0.215825 | -0.211144 | -0.206462 | -0.201781 | -0.197099 | -0.192417 | -0.187736 | -0.183054 | -0.178373 | -0.173691 | -1.690094e-01 |
| 17 | 1.789474 | -2.566038e+00 | -2.561533 | -2.557028 | -2.552523 | -2.548018 | -2.543513 | -2.539008 | -2.534503 | -2.529998 | -2.525493 | -2.520988 | -2.516484 | -2.511979 | -2.507474 | -2.502969 | -2.498464 | -2.493959 | -2.489454 | -2.484949 | -2.480444 | -2.475939 | -2.471434 | -2.466929 | -2.462424 | -2.457920 | -2.453415 | -2.448910 | -2.444405 | -2.439900 | -2.435395 | -2.430890 | -2.426385 | -2.421880 | -2.417375 | -2.412870 | -2.408365 | -2.403860 | -2.399355 | -2.394851 | ... | -0.489267 | -0.484762 | -0.480257 | -0.475752 | -0.471247 | -0.466743 | -0.462238 | -0.457733 | -0.453228 | -0.448723 | -0.444218 | -0.439713 | -0.435208 | -0.430703 | -0.426198 | -0.421693 | -0.417188 | -0.412683 | -0.408179 | -0.403674 | -0.399169 | -0.394664 | -0.390159 | -0.385654 | -0.381149 | -0.376644 | -0.372139 | -0.367634 | -0.363129 | -0.358624 | -0.354119 | -0.349614 | -0.345110 | -0.340605 | -0.336100 | -0.331595 | -0.327090 | -0.322585 | -0.318080 | -3.135751e-01 |
| 18 | 1.894737 | -2.618182e+00 | -2.613841 | -2.609500 | -2.605158 | -2.600817 | -2.596476 | -2.592135 | -2.587794 | -2.583453 | -2.579112 | -2.574771 | -2.570430 | -2.566088 | -2.561747 | -2.557406 | -2.553065 | -2.548724 | -2.544383 | -2.540042 | -2.535701 | -2.531360 | -2.527019 | -2.522677 | -2.518336 | -2.513995 | -2.509654 | -2.505313 | -2.500972 | -2.496631 | -2.492290 | -2.487949 | -2.483607 | -2.479266 | -2.474925 | -2.470584 | -2.466243 | -2.461902 | -2.457561 | -2.453220 | ... | -0.616930 | -0.612589 | -0.608248 | -0.603907 | -0.599566 | -0.595225 | -0.590884 | -0.586542 | -0.582201 | -0.577860 | -0.573519 | -0.569178 | -0.564837 | -0.560496 | -0.556155 | -0.551814 | -0.547472 | -0.543131 | -0.538790 | -0.534449 | -0.530108 | -0.525767 | -0.521426 | -0.517085 | -0.512744 | -0.508402 | -0.504061 | -0.499720 | -0.495379 | -0.491038 | -0.486697 | -0.482356 | -0.478015 | -0.473674 | -0.469332 | -0.464991 | -0.460650 | -0.456309 | -0.451968 | -4.476269e-01 |
| 19 | 2.000000 | -2.666667e+00 | -2.662478 | -2.658289 | -2.654100 | -2.649912 | -2.645723 | -2.641534 | -2.637345 | -2.633156 | -2.628968 | -2.624779 | -2.620590 | -2.616401 | -2.612212 | -2.608024 | -2.603835 | -2.599646 | -2.595457 | -2.591268 | -2.587080 | -2.582891 | -2.578702 | -2.574513 | -2.570324 | -2.566136 | -2.561947 | -2.557758 | -2.553569 | -2.549381 | -2.545192 | -2.541003 | -2.536814 | -2.532625 | -2.528437 | -2.524248 | -2.520059 | -2.515870 | -2.511681 | -2.507493 | ... | -0.735634 | -0.731446 | -0.727257 | -0.723068 | -0.718879 | -0.714690 | -0.710502 | -0.706313 | -0.702124 | -0.697935 | -0.693746 | -0.689558 | -0.685369 | -0.681180 | -0.676991 | -0.672803 | -0.668614 | -0.664425 | -0.660236 | -0.656047 | -0.651859 | -0.647670 | -0.643481 | -0.639292 | -0.635103 | -0.630915 | -0.626726 | -0.622537 | -0.618348 | -0.614159 | -0.609971 | -0.605782 | -0.601593 | -0.597404 | -0.593216 | -0.589027 | -0.584838 | -0.580649 | -0.576460 | -5.722716e-01 |
20 rows × 502 columns
t = dataset.input_dataset.to_numpy()[:, 0]
u_t = dataset.output_dataset.to_numpy()
t_split = 0.87
Plot dataset¶
def lines_gen():
"""Linestyle generator."""
yield "-"
for i in range(1, dataset.n_samples):
yield 0, (i, 1, 1, 1)
color = "red"
lines = lines_gen()
for i in range(dataset.n_samples):
# Switch mode if discontinuity is gone
if color == "red" and t[i] > t_split:
color = "blue"
lines = lines_gen() # reset linestyle generator
plt.plot(u_t[i], color=color, linestyle=next(lines), label=f"t={t[i]:.2f}")
plt.legend()
plt.title("Solutions to Burgers equation")
plt.show()
Create KLSVD¶
n_modes = 7
klsvd = KLSVD(dataset.misc["x"], n_modes)
klsvd.fit(u_t)
u_t_reduced = klsvd.transform(u_t)
u_t_restored = klsvd.inverse_transform(u_t_reduced)
f"Dimension of the reduced space: {klsvd.output_dimension}"
'Dimension of the reduced space: 7'
Plot restored data¶
color = "red"
lines = lines_gen()
for i in range(dataset.n_samples):
# Switch mode if discontinuity is gone
if color == "red" and t[i] > t_split:
color = "blue"
lines = lines_gen() # reset linestyle generator
plt.plot(
u_t_restored[i],
color=color, # linestyle=next(lines),
label=f"t={t[i]:.2f}",
)
plt.legend()
plt.title("Reconstructed solution after KLSVD reduction.")
plt.show()
Total running time of the script: (0 minutes 0.698 seconds)